Unsaturated Conductivity

There are three optional ways of determining the unsaturated hydraulic conductivity in the model (see switch Conductivity Function).

Following Mualem (1976), the unsaturated conductivity, k_w^*, is given by:

                                                        (2.26)

If the Brooks & Corey function for water retention is used, eq.(2.19), the unsaturated conductivity, k_w^*, can then be expressed as:

                                                   (2.27)

where k_mat is the saturated matrix conductivity and n is a parameter accounting for pore correlation and flow path tortuosity. Eqs. (2.26)- (2.28) are used for water contents in the matric pores.

See viewing functions Measured Unsaturated Conductivity, Pressure Head, single layers, Measured Unsaturated Conductivity, Water Content, single layers and Modelled Unsaturated Hydraulic Conductivity, profile.

In case of using the van Genuchten equation, eq. (2.21), the corresponding equation for the unsaturated conductivity is given by:

                          (2.28)

where the coefficients α, g_n and g_m are the same parameters as used in eq (2.21)..

As alternative options to the equations of Mualem eqs. (2.26)- (2.28)   the unsaturated hydraulic conductivity, k_w^*, can either be caluclated as a simple power function of relative saturation:

                                                         (2.29)

or as a simple power function of effective saturation:

                                                             (2.30)

where p_nr and p_ne are parameters, k_mat is the saturated matrix conductivity, θ_s is the water content at saturation, θ is the actual water content and S_e is the effective saturation.

Figure 2.4. The unsaturated conductivity for a clay soil calculated with the parameter values given above.

To account for the conductivity in the macropores, an additional contribution to the hydraulic conductivity is considered when water content exceeds θ_s - θ_m, i.e. at ψ_mat (see Figure 2.4 above). The total hydraulic conductivity close to saturation is thus calculated as:

                                  (2.31)

where k_sat is the saturated total conductivity, which includes the macropores, and k_w^*(θ_s - θ_m) is the hydraulic conductivity below θ_s - θ_m (i.e. at ψ_mat) calculated from eqs (2.26)- (2.28).

All the hydraulic conductivities are scaled with respect to temperature. The scaling is related to the viscosity of water and is simplified to a linear response in the normal range around 20 °C, which is used as a reference temperature. In addition to this dependence a minimum unsaturated conductivity is also applied. Thus the actual unsaturated hydralic conductivity after temperature corrections, k_w, is given by:

                                   (2.32)

where r_AOT, r_A1T and k_minuc are parameter values. k_w^* is the conductivity according to eqs. (2.26)-(2.31). See viewing function Hydraulic conductivity, temperature function.